Simon Willerton

Preprints

• Spread: a measure of the size of metric spaces
  arxiv:1209.2300 [Blogpost]
• Heuristic and computer calculations for the magnitude of metric spaces
  arxiv:0910.5500 [Blogpost]

Research Publications

• Tight spans, Isbell completions and semi-tropical modules
  Theory and Applications of Categories 28 (2013) 696-732. arxiv:1302.4370 [Blogpost]
• On the magnitude of spheres, surfaces and other homogeneous spaces
  Geometriae Dedicata (2013). arxiv:1005.4041 [Blogpost]
• On the asymptotic magnitude of subsets of Euclidean space (with Tom Leinster)
  Geometriae Dedicata 164 (2013) 287-310. arxiv:0908.1582 [Blogpost]
• The Mukai pairing, I: a categorical approach (with A.Caldararu),
  New York Journal of Mathematics 16 (2010) 61-98. arXiv:0707.2052
• On the Rozansky-Witten weight systems (with J.Roberts),
  Algebraic & Geometric Topology 10 (2010) 1455-1519. math.DG/0602653. See also Justin Roberts' talk.
• A diagrammatic approach to Hopf monads
  [For less wide typesetting style see arXiv version.]
  Arabian Journal of Science and Engineering C - Theme Issue "Interactions of algebraic and coalgebraic structures (theory and applications)" December 2008; Vol. 33, Number 2C math/0807.0658
• The twisted Drinfeld double of a finite group via gerbes and finite groupoids
  Algebraic & Geometric Topology 8 (2008) 1419-1457 math.QA/0503266
• Gerbes and Homotopy Quantum Field Theories (with U.Bunke and P.Turner)
  Algebr. Geom. Topol. 4 (2004) 407-437 math/0201116
• Homotopy quantum field theories and related ideas (with M.Brightwell and P.Turner)
  Int. J. Modern Phys. A 18 Supplement (2003) 115-122.
• An almost-integral universal Vassiliev invariant of knots
  Algebraic and Geometric Topology 2 (2002) paper no. 29, 649-664 math/0105190
• On the first two Vassiliev invariants,
  Experimental Mathematics (2002).
• Free groups and finite type invariants of pure braids (with J.Mostovoy)
  Math. Proc. Camb. Phil. Soc. 132 (2001) 117-130.
• The Kontsevich integral and algebraic structures on the space of diagrams,
  Knots in Hellas '98, Series on Knots and Everything vol 24, World Scientific, 2000, 530-546.
• Vassiliev invariants as polynomials,
  Knot Theory, Banach Centre Publications 42 (1998) 457-463.
• A combinatorial half-integration from weight system to Vassiliev knot invariant,
  J. Knot Theory Ramifications, 7 no. 4 (1998) 519-526.
• Vassiliev invariants and the Hopf algebra of chord diagrams,
  Math. Proc. Camb. Phil. Soc., 119 (1996) 55-65.

Popularizations

• A topological tie-in,
  Nature 368 103-104, 10 March 1994.

Unpublished

• On the Vassiliev invariants for knots and for pure braids,
  (official abstract) Edinburgh University PhD Thesis, July 1997. This contains material from the above papers together with ideas on the relationship between Vassiliev invariants for pure braids and de Rham homotopy theory.
• Vassiliev invariants for knots,
  Essay for Part III of the Cambridge Mathematical Tripos, May 1993. A survey of Bar-Natan's paper On the Vassiliev knot invariants, which contained some additional work of my own.

Talks

• Magnitude and other measures of metric spaces, July 2012.
• Magnitude of Metric Spaces II, September 2010.
  A prequel to this talk, Magnitude of Metric Spaces I, was given by Tom Leinster.
• Two 2-traces August 2008.
  There are two videos of this talk on YouTube:
  • Oxford August 2008
  • Birmingham September 2010

Selected writings at the n-Category Café

Formal Concept Analysis (Sep 2, 2013)

Have a peek at the notion of formal concept analysis

The Nucleus of a Profunctor: Some Categorified Linear Algebra (Aug 19, 2013)

Watch some linear algebra being categorified.

Torsors and enriched categories (Jun 3, 2013)

Read about a different take on torsors

Project Scheduling and Copresheaves (Mar 24, 2013)

Find out what PERT graphs have to do with enriched categories

Tight spans, Isbell completions and semi-tropical modules (Jan 20, 2013)

See how these three things are related.

The Spread of a Metric Space (Sep 5, 2012)

Read how this notion of size for metric spaces has some interesting properties.

Integral Transforms and the Pull-Push Perspective, I (Nov 7, 2010)

Start to see how enriched profunctors can be viewed as categorifications of integral kernels.

Enriching Over a Category of Subsets (Aug 30, 2010)

Discover how enriched category theory leads to the definition of some generalized metrics on the space of continuous functions on the unit interval.

On the Magnitude of Spheres, Surfaces and Other Homogeneous Spaces (Apr 21, 2010)

See the details of a new paper on the magnitude of metric spaces.

Modeling Surface Diagrams (Mar 24, 2010)

Watch some videos to see how I’m trying to make 3d models of categorical surface diagrams.

Intrinsic Volumes and Weyl's Tube Formula (Mar 12, 2010)

Read about how the volume of a tube around a surface in 3-space depends only on intrinsic invariants of the surface.

A Look at the Mathematical Origins of Western Musical Scales (Feb 26, 2010)

See how the rational numbers 2 and 3/2 gave birth to the Western musical scale.

More Magnitude of Metric Spaces and Problems with Penguins (Oct 10, 2009)

Learn about the tenuous link between emperor penguins and the magnitude of metric spaces.